UNSPECIFIED (2002) McKay correspondence. ASTERISQUE (276). 53-+. ISSN 0303-1179

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Abstract

Let M be a quasiprojective algebraic manifold with K-M = 0 and G a finite automorphism group of M acting trivially on the canonical class K-M; for example, a subgroup C of SL(n, C) acting on C-n in the obvious way. We aim to study the quotient variety X = M/G and its resolutions Y --> X (especially under the assumption that Y has K-Y = 0) in terms of G-equivariant geometry of Al. At present we know 4 or 5 quite different methods of doing this, taken from string theory, algebraic geometry, motives, moduli, derived categories, etc. For G in SL (n, C) with n = 2 or 3, we obtain several methods of cobbling together a basis of the homology of Y consisting of algebraic cycles in one-to-one correspondence with the conjugacy classes or the irreducible representations of G.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ASTERISQUE
Publisher:	SOC MATHEMATIQUE FRANCE
ISSN:	0303-1179
Date:	2002
Number:	276
Number of Pages:	21
Page Range:	53-+
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/11240

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